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Correct, the best way to see this is draw a circle or elipse. Place the Sun and Earth opposite each other somewhere on the circumference. Note this as there "real" positions. Now mark where an observer on the Sun see's the Earth, say a centimetre anti-clockwise, likewise mark where an observer on Earth sees the Sun, also a centimetre anti-clockwise. Repeat this for an point in time drawing a line between the "real" Earth and Sun positions and the relativistically observable Earth and Sun posiitons. For any points you get a stable, balanced system with a stable point of suspension, so the system doesn't collapse.
Nice how nature works out all the complex mathematics for us, isn't it! And as you noted, it wasn't a question, more an interesting observation of something I bothered to research about a year ago!
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